In the field of adaptive notch filtering, Monotonically Increasing Gradient (MIG) algorithm has recently been proposed by Sugiura and Shimamura [1], where it is claimed that the MIG algorithm shows monotonically increasing gradient characteristics. However, our analysis has found that the underlying theory in [1] includes crucial errors. This letter shows that the formulation of the gradient characteristics in [1] is incorrect, and reveals that the MIG algorithm fails to realize monotonically increasing gradient characteristics when the input signal includes white noise.